Adjusted complex position of extra sources in the image sources method

Using a series development of the integral solution, a formal backing of the presence of image sources in geometrical acoustics methods has been shown. Furthermore, the existence of "invisible" sources is suggested, especially in the vicinity of obtuse angles. These extra sources bring useful information but need to be adjusted in order to avoid divergences. By more closely comparing the terms of the series development and the corresponding image source, the position of each extra source can be adjusted so as to minimize the distance between term and source contribution. In other words, a correction factor must be applied to the pure geometrical position of the "invisible" sources. In order to obtain the best results, this position may need to be defined as a complex number. This approach could have a companion idea in electromagnetism, where a function is identified with the objective of optimizing the position of the image sources.